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Large deviations for product of sums of random variables |
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| Affiliation: | 1. Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada L8S 4K1;2. Institute of Statistics, RWTH Aachen University, 52056 Aachen, Germany;3. Department of Statistics and Insurance Science, University of Piraeus, 80 Karaoli & Dimitriou str., 18534 Piraeus, Greece;4. Department of Statistics, King Abdulaziz University, Jeddah, Saudi Arabia;1. Department of Basic and Applied Sciences for Engineering, Sapienza University of Rome, Italy;2. Department of Statistical Sciences, Sapienza University of Rome, Italy |
| Abstract: | In this paper, we obtain sample path and scalar large deviation principles for the product of sums of positive random variables. We study the case when the positive random variables are independent and identically distributed and bounded away from zero or the left tail decays to zero sufficiently fast. The explicit formula for the rate function of a scalar large deviation principle is given in the case when random variables are exponentially distributed. |
| Keywords: | Large deviations Sample paths Product of sums of random variables |
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